It may be one of the variable camshaft timing solenoids going bad. How many miles does your Mustang have? A bad VCT solenoid will not throw a code. As a diagnosis, you can unplug the solenoids on both sides of the engine and drive with them that way. The car will be stuck on idle timing as you drive so there will be a loss of power but if the car acts normally after you come to a stop with the solenoids unplugged, then you know they are the problem. One of them is most likely sticking on and making your timing stuck on advanced position when you come to a stop, which will cause hesitation, tapping noises, and overall a bad running engine. The same thing was happening to me recently and it was all fixed when I replaced the passenger side VCT solenoid.
Here are two recently posted youtube videos that helped me.
Keep in mind that your problem can be a range of things but I have some experience with my 4.6 engine and what you described to me seems like the VCT solenoid. Your problem can also be a dirty throttle body or a bad throttle position sensor, among other things.
Also, cool to see you are in Florida
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